Question

The ratio of the diagonals of a rhombus is 3:4 and its area is 384 cm^2. find its diagonals

Answer 1

Let diagonal 1 (d 1) = 3x cm
diagonal 2 (d 2)= 4x cm

Area of rhombus = 1/2*d1*d2

➡384 = 1/2*3x*4x

➡384 = 3x*2x

➡384 = 6x^2

➡384/6 = x^2

➡64 = x^2

➡√64 = x

➡8 = x

diagonal 1 = 3x = 3*8 = 24 cm
diagonal 2 = 4x = 4*8 = 32cm

Answer 2

Answer:

Here ,

Let Diagonal 1 (d₁ ) = 4x

And Diagonal 2 (d₂ ) = 3x

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As we know that

Area of a rhombus =$\frac{1}{2}$ × d₁ ₓ d₂

→ 384 =  $\frac{1}{2}$× 4x × 3x

→ 384 × 2 = 12x²

→ 768 = 12x²

→ x² =   $\frac{768}{12}$

→ x² = 64

→ x = √64

→ x = 8

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Then ,

d₁ = 4x = 4 × 8 = 32 cm

d₂ = 3x = 3 × 8 = 24 cm

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